Modern computer applications require not only to protect data using encryption, but also to perform computations on data in encrypted form, e.g., in a cloud computing setting where private data is stored and processed on a remote, untrusted server. Lattice cryptography is a fast-developing area of mathematical cryptography which has the potential to deliver new and better solutions to many complex security problems, and currently the only known technique allowing the construction of fully homomorphic encryption schemes: encryption mechanisms that allow to perform arbitrary computations on encrypted data. Lattice cryptography also offers post-quantum security, i.e., it is believed to resist the future threat posed by the development of quantum computers. The project's novelties are the introduction of a new framework for the design and analysis of homomorphic encryption functions, and its use to improve the understanding of this important cryptographic primitive, as well as to improve its efficiency. The project impacts are enabling better methods to securely share and use data (in encrypted form), and inform ongoing efforts to standardize post-quantum cryptography and homomorphic encryption. This project investigates a general framework for the modular design of complex cryptographic primitives based on lattices, including fully homomorphic encryption (FHE). Starting from a basic (private key) encryption scheme satisfying certain weak linear homomorphic properties, a variety of known homomorphic encryption schemes, as well as some new ones, are described in a unified, modular way, compared, analyzed and combined. Within this framework, several important problems are investigated. Specific questions considered in this project are: the design of circular secure FHE schemes, the construction of more efficient FHE schemes making use of amortized bootstrapping techniques, the use of hybrid solutions combining together different FHE schemes as well as forms of secure multiparty computation based on secret sharing, and the construction of multi-use universally composable oblivious transfer based on lattices.
SaTC: CORE: Small: Modular, Efficient, Homomorphic Cryptography